We have presented a scalable DD approach to tackle the issue of discontinuous B-spline based MFA representations when performing the computations in parallel. The Restricted Additive Schwarz (RAS) method is a natural algorithmic fit for data analysis problems to create efficient MFA solutions in parallel. Through the use of Schwarz-based iterative schemes, combined with constrained local subdomain solvers, the two-level iterative technique has been shown to be robust in converging to the compressed functional representation of the given data, without sacrificing the approximation accuracy measured on a single subdomain of equivalent control point resolution. Replacing B-spline bases with NURBS bases (\(W \ne 1\) ) only requires imposing the constraints on the \(\vec{P}_i W_i\)  data instead of \(\vec{P}_i\)  alone, which is naturally accomplished with minor modifications in Algorithm (REF ). This can also be combined with aposteriori error measures [1]} to adaptively resolve solution variations while ensuring higher-order continuity across subdomain boundaries with appropriate knot insertion, removal and communication of shared DoFs in \(\Delta \cup \delta \)  regions. Another natural way to ensure continuity across adaptively resolved NURBS or B-spline patches would be to use T-splines [2]}, which are specifically designed for merging higher-dimensional surfaces with non-matching knot locations. All presented ideas should extend for T-splines instead of B-splines as well with modifications to \(\mathcal {C}\)  in Equation (REF ).
